On the Fractal Geometry of Gait Dynamics in Different Neuro-degenerative Diseases

Neuro-degenerative diseases influence significantly the gait behavior and the ability to move. To explore the etiology of neuro-degenerative disease, it would be useful to characterize gait dynamics. The purpose of this study is to classify different neuro-degenerative diseases using fractal geometry. We use Gait Dynamics in Neuro-Degenerative Disease Data Base including recordings from patients with Parkinson’s disease (n = 15), Huntington’s disease (n = 20), or amyotrophic lateral sclerosis (n = 13) and 16 healthy control subjects are also included (Hausdorff JM et al., 2000). The vibration analysis using power spectral densities (PSD) method has been carried out to discover whether some type of power-law scaling exists for various statistical moments at different scales of these databases. Using Discrete Wavelet Transform (DWT) and Wavelet Leader Multifractal (WLM) analysis, we explore the possibility that these recordings belong to the class of multifractal process for which a large number of scaling exponents are required to characterize their scaling structures. A non-linear analysis called the Fractal Dimension (FD) using Higuchi algorithm has been performed to quantify the fractal complexity of recordings. According to our results, we noticed that neither the power spectral densities nor the Higuchi algorithm to find the fractal dimension alone were sufficient to separate different classes of patients and healthy people. In addition, when multifractal analysis and scaling exponent were used as a classifier, the three classes could not be well separated. However, this study revealed that we have a wide range of exponents for some of the gait recordings which indicates they have multifractal structure and they need to be indexed by different exponents as we decompose them into different subsets. In other words, these multifractal subjects require much more exponents to characterize their scaling properties compared to monofractal gait recordings which their spectrum displays a narrow width of scaling exponent. Another important outcome from our multifractal analysis is recognizing obvious changes in the shape of D(h) curves for some of the gait recordings which is crucial in finding the best strategies to better controlling the gait mechanisms in different neuro-degenerative diseases. Although the vibration analysis, fractal dimension and multifractal analysis may not be able to classify gait recordings, however, they can be used as comprehensive frameworks to further analysis, characterize and compare the complexity and fractal behavior of gait recordings and data structures of different neuro-degenerative diseases in clinical database. Likewise, beside the Higuchi algorithm to find the fractal dimension as a complexity measure for the gait recordings, it will require much more efforts and further clinical analysis to find a specific threshold which make the fractal dimension to be considered as a biomarker and diagnosis tool for different neuro-degenerative diseases.